WHAT’S IN AN AREA 2
TEACHER EDITION
List of Activities for this Unit:
ACTIVITY / STRAND / DESCRIPTION1 – Don’t be Square / ME & AS / Finding the area of squares.
2 – Quadrangle Regions / ME & AS / Finding the area of rectangles.
3 - Loop the Neighborhood / ME & AS / Finding the area of circles.
4 - Alter the Breadth / ME & AS / Investigate the affect on the area of changing a dimension of a square, rectangles, and circles.
5 – Region Locale / ME & AS / Area problems in context.
6 – Multiple Choice Items / ME & AS / Several multiple choice area problems.
COE Connections
MATERIALS / Calculators
Warm-Ups
(in Segmented Extras Folder)
Length of Lesson: 200 minutes
Vocabulary: Mathematics & ELL
area / lengthcenter / perimeter
circumference / square units
designed / radius
diameter / rectangle
dimensions / ruptured
double side / tethered
enlargement / triple side
grid paper / width
heritage / π
irregular
Essential Questions:
· What does area mean?
· How do you determine the area of a square?
· How do you determine the area of a perimeter?
· What is a diameter of a circle?
· What is the radius of a circle?
· How does radius and diameter relate to each other?
· How do you determine the area of a circle?
· What is meant by leaving the area of a circle in terms of pi?
· How does the change in one linear dimension affect the area?
· How can a conclusion be supported using mathematical information and calculations?
Lesson Overview:
· Before allowing the students the opportunity to start the activity: access their prior knowledge regarding how to doing an investigation. Access their prior knowledge with regards to using area in everyday situations.
· A good warm-up for this activity is .
· What would happen if one linear dimension of a square, rectangle or circle is changed?
· How is a problem situation decoded so that a person understands what is being asked?
· What mathematical information should be used to support a particular conclusion?
· How will the students make their thinking visible?
· Use resources from your building.
Performance Expectations:
4.3.C Determine the perimeter and area of a rectangle using formulas, and explain why the formulas work.
4.3.D Determine the areas of figures that can be broken down into rectangles.
4.3.F Solve single- and multi-step word problems involving perimeters and areas of rectangles and verify the solutions.
6.4.A Determine the circumference and area of circles.
6.4.C Solve single- and multi-step word problems involving the relationships among radius, diameter, circumference, and area of circles, and verify the solutions.
7.2.C Describe proportional relationships in similar figures and solve problems involving similar figures.
7.2.D Make scale drawings and solve problems related to scale.
7.3.C Describe the effect that a change in scale factor on one attribute of a two- or three-dimensional figure has on other attributes of the figure, such as the side or edge length, perimeter, area, surface area, or volume of a geometric figure.
8.4.C Evaluate numerical expressions involving non-negative integer exponents using the laws of exponents and the order of operations.
Performance Expectations and Aligned Problems
Chapter 11 “What’s in an Area 2” Subsections: / 1-Don’t be Square / 2- Quadrangle Regions / 3-
Loop the Neighbor-hood / 4 –
Alter the Breadth / 5 –
Region Locale / 6 –
MC Items
Problems Supporting:
PE 4.3.C / 1 / 2 / 5, 6 (parts of) / 8, 10, 11, 13 / 14, 22
Problems Supporting:
PE 4.3.D / 1 / 2 / 14
Problems Supporting:
PE 4.3.F / 5, 6 (parts of) / 10, 11, 13 / 14
Problems Supporting:
PE 6.4.A / 3, 4 / 7 / 12 / 17, 18
Problems Supporting:
PE 6.4.C / 3, 4 / 7 (parts of) / 9, 12 / 17, 18
Problems Supporting:
PE 7.2.C / 7 (parts of) / 9, 12 / 15, 16, 19, 20, 22, 23
Problems Supporting:
PE 7.2.D / 5-7 (parts of) / 8-13 / 15, 16, 19, 20, 22, 23
Problems Supporting:
PE 7.3.C / 5-7 (parts of) / 8-13 / 15, 16, 19, 20, 22, 23
Problems Supporting:
PE 8.4.E / 1 / 4 / 5-7 (parts of) / 9, 12 / 14, 18, 19, 23
Assessment: Use the multiple choice and short answer items from Number Sense and Algebraic Sense that are included in the CD. They can be used as formative and/or summative assessments attached to this lesson or later when the students are being given an overall summative assessment.
Don’t be Square
1. How do you find the area of a square? Area is the number of square units that it takes to cover a figure.
a. Mr. Warren is building a pen for his dog, Jake. The pen will be in the shape of a square
that is 9 ft. by 9 ft. Draw the square on grid paper that represents the pen. How much area
will the dog pen contain? ______81 ft²______
Support your answer using words numbers and/or diagrams.
b. Rather than count the number of squares inside the pen that you drew in question 1a, there
is a shorter method you can apply to calculate the area of a square. What is that method?
_____L × W = A (L = length, W = width, A = Area) OR S² = A_(S = Side)______
c. What is the area of a square with sides of length 4 inches? ___16 in²______
Support your answer using words, numbers and/or diagrams.
4² = A
16 = A
d. What is the length of each side of a square that has an area of 81in2? ___9______
Support your answer using words, numbers and/or diagrams.
A = S²
81 = S2
e. What is the area of a square with sides of length s ft? _____S²______
Support your answer using words, numbers and/or diagrams.
A = S²
f. What is the length of each side of a square that has an area of A ft2? ______
Support your answer using words, numbers and/or diagrams.
Quadrangle Regions
2. How do you find the area of a rectangle?
a. Mr. Warren’s daughter prefers a rectangular shaped pen for their dog. She proposes that the pen measure is 9 ft. by 8 ft. Draw the rectangle on grid paper that represents the pen. How much area will the dog pen contain? _____72 ft²______
Support your answer using words numbers and/or diagrams.
b. What is the area of a rectangle with a width of 5 inches and a length of 12 inches? _60 in²_
Support your answer using words, numbers and/or diagrams.
5 × 12 = A
60 = A
c. What is the width of a rectangle that has a length of 9 inches and an area of 72 in2? _8 in_
Support your answer using words, numbers and/or diagrams.
L ´ W = A
9 ´ W = 72
W = 8
d. What is the area of a rectangle with a width of w inches and a length of l inches? _L ´ W
Support your answer using words, numbers and/or diagrams.
L ´ W = A
e. What is the width of a rectangle that has a length of l inches and an area of A in2? ______
Support your answer using words, numbers and/or diagrams.
f. Jonie wants to cover the bulletin board with bright paper. The bulletin board measures 4 ft by 3 ft. What is the area of the bulletin board? ____12 ft²______
Support your answer using words, numbers and/or diagrams.
3 ´ 4 = A
12 = A
Loop the Neighborhood
3. What is meant by the area of a circle? When you want to determine the amount of material that it would take to cover a circle, you are looking for the area of a circle. The units in your answer will be square units. You could draw a circle on a grid and count the squares to determine the area, but that can be difficult because a circle doesn’t perfectly fit the grid squares. There is a formula that can be used to determine the area of a circle.
a. What is the formula we could use to determine the area of a circle? __A = r²p___
4. Some terminology regarding a circle needs to be understood.
a. What point appears to be the center of the circle? ____A______
b. Name 2 diameters. ______
c. Name a radius ______Name another radius ______
(possible answers)
d. If a diameter is 10 units long, how long is the radius? ___5 units______
e. If a radius is eight units long, how long is the diameter? _16 units______
f. What is the area of a circle with a radius of 5 feet? __25p or 78.54 or 78.75 ft²____
Support your answer using words, numbers and/or diagrams.
A = r²p
A = 5²×p
A = 25p or 78.54 or 78.75
g. What is the area of a circle with a diameter of 12 feet? _36p or 113.097 or 113.04 ft²___
Support your answer using words, numbers and/or diagrams.
D = 12ft
r = ½ × 12 = 6
A = r²p
A = 6²p
A = 36p or 113.097 or 113.04 ft²
h. What is the radius of a circle with an area of 36π cm2? ____6 cm______
Support your answer using words, numbers and/or diagrams.
A = r²p
36p = r²p
i. What is the diameter of a circle with an area of 81π cm2? _____18 cm______
Support your answer using words, numbers and/or diagrams.
A = r²p
81p = r²p
j. The diameter of a quarter is 28 millimeters. What is the area of one surface of the quarter?
_____196pmm or 615.75 mm or 615.44 mm²______
Support your answer using words, numbers and/or diagrams.
D = 28mm A =14²×p
r = ½ (28) A = 196p or 615.75 or 615.44
r = 14mm
k. Bernard must make two circular tablecloths for a reception. The diameter of each
table must be 14 feet and there needs to be a 1 foot overhang. How many square feet of
fabric must be used to make the two tablecloths? __128p or 402.12 or 401.92 ft²___
Support your answer using words, numbers and/or diagrams.
d = 14 ft + 2 ft A = 8²p
r = 7 ft + 1 ft = 64p or 201.06 or 200.96
r = 8 ft 2 (64p) or 402.12 or 401.92
Alter the Breadth
5. Use the square below the table to complete the table.
Length of side / Area / Change in side / New LengthOf Side / New Area / Describe area change
2 cm. / 4 cm.2 / Double side / 4 cm / 16 cm 2 / 4 times as big
2 cm. / 4 cm² / Triple side / 6 cm / 36 cm² / 9 times as big
5in / 25 in 2 / Double side / 10 in / 100 cm² / 4 times as big
4 m. / 16 m² / Multiply sides by 4 / 16 m / 256 m² / 16 times as big
7 in / 49 in 2 / Multiply sides by 5 / 35 in / 1225 in² / 25 times as big
2.5 m. / 6.25 m² / Multiply sides by 10 / 25 m / 625 m² / 100 times as big
12 ft. / 144 ft² / Multiply sides by 3 / 36 ft / 1296 ft² / 9 times as big
K / K² / Multiply side by m / km / k²m² / m² times as big
6. Use the rectangle below the table to complete the table.
A / B / Area / Change in length of sides A & B / New Area / New Length of Side A / New Length of Side B / Describe perimeter change / Describe area change3 cm / 5 cm. / 15 cm2 / Double both sides / 60 cm2 / 6 cm / 10 cm / Perimeter doubles / 4 times as big
2” / 7” / 14 in² / Multiply both sides by 3 / 126 cm² / 6” / 21” / 54 vs. 18
Perimeter triples / 9 times as big
4.3m / 8m / 34.4 m2 / Multiply both sides by 4 / 550.4 m² / 17.2 m / 32 m / 98.4 vs. 24.6
Perimeter Quadruples / 16 times as big
6 in / / 40 in2 / Multiply both sides by 3 / 360 in² / 18 in / 20 in / 76" vs. in
Perimeter triples / 9 times as big
7 ft. / 10 ft. / 70ft.2 / Multiply both sides by 6 / 2520 ft² / 42 ft / 60 ft / 204 ft. vs. 34 ft.
Perimeter is 6 times as big / 36 times as big
3 cm / 4 cm / 12 cm² / Multiply both sides by 5 / 300 cm2 / 15 cm / 20 cm / 70 cm vs. 14 cm
Perimeter is 5 times as big / 25 times as big
2 ft. / 5 ft. / 10 ft.² / Multiply A by 2 and B by 5 / 100 ft. 2 / 4 ft / 25 ft / 58 ft. vs. 14 ft. / 10 times (5×2) as big
A / B / AB / Multiply both sides by 3 / 9AB / 3A / 3B / 2A + 2B vs. 6A + 6B
Perimeter triples / 9 times as big
A
7. Use the circle below the table to help complete the table.